A comparative study of confidence intervals for negative binomial proportion

In this paper, we investigate four existing and three new confidence interval estimators for the negative binomial proportion (i.e., proportion under inverse/negative binomial sampling). An extensive and systematic comparative study among these confidence interval estimators through Monte Carlo simulations is presented. The performance of these confidence intervals are evaluated in terms of their coverage probabilities and expected interval widths. Our simulation studies suggest that the confidence interval estimator based on saddlepoint approximation is more appealing for large coverage levels (e.g., nominal level≤1% ) whereas the score confidence interval estimator is more desirable for those commonly used coverage levels (e.g., nominal level>1% ). We illustrate these confidence interval construction methods with a real data set from a maternal congenital heart disease study.     

Mean shift and influence measures in linear measurement error models with stochastic linear restrictions

We present influence diagnostics for linear measurement error models with stochastic linear restrictions using the corrected likelihood of Nakamura in 1990. The case deletion and mean shift outlier models are developed to identify outlying and influential observations. We derive a corrected score test statistic for outlier detection based on mean shift outlier models. The analogs of Cook's distance and likelihood distance are proposed to determine influential observations based on case deletion models. A parametric bootstrap procedure is used to obtain empirical distributions of the test statistics and a simulation study has been used to evaluate the performance of the proposed estimators based on the mean squares error criterion and the score test statistic. Finally, a numerical example is given to illustrate the theoretical results.     

Interval estimation for the breakpoint in segmented regression: a smoothed score‐based approach

This paper is concerned with interval estimation for the breakpoint parameter in segmented regression. We present score‐type confidence intervals derived from the score statistic itself and from the recently proposed gradient statistic. Due to lack of regularity conditions of the score, non‐smoothness and non‐monotonicity, naive application of the score‐based statistics is unfeasible and we propose to exploit the smoothed score obtained via induced smoothing. We compare our proposals with the traditional methods based on the Wald and the likelihood ratio statistics via simulations and an analysis of a real dataset: results show that the smoothed score‐like statistics perform in practice somewhat better than competitors, even when the model is not correctly specified.     

Asymptotic relative efficiency of wald tests in measurement error models

In this paper, asymptotic relative efficiency (ARE) of Wald tests for the Tweedie class of models with log-linear mean, is considered when the aux¬iliary variable is measured with error. Wald test statistics based on the naive maximum likelihood estimator and on a consistent estimator which is obtained by using Nakarnura's (1990) corrected score function approach are defined. As shown analytically, the Wald statistics based on the naive and corrected score function estimators are asymptotically equivalents in terms of ARE. On the other hand, the asymptotic relative efficiency of the naive and corrected Wald statistic with respect to the Wald statistic based on the true covariate equals to the square of the correlation between the unobserved and the observed co-variate. A small scale numerical Monte Carlo study and an example illustrate the small sample size situation.     

Efficiency or Competition? A Structural Econometric Analysis of Canada's AWS Auction and the Set‐Aside Provision

In 2008, Industry Canada auctioned 105 MHz of spectrum to a group of bidders that included incumbents and potential new entrants into the Canadian mobile phone market, raising $4.25 billion. In an effort to promote new entry, 40 MHz of spectrum was set‐aside for new entrants. In order to estimate the implicit cost of the set‐aside provision, we estimate the parameters of the bidders' profit function via a maximum match estimator based on the notion of pairwise stability in matches. We find that all telecommunications firms valued both geographic complementarities across auction licenses as well as absolute spectrum. Under a reasonable alternative scenario, our results indicate that the set‐aside led to a total profit loss of approximately 10%.     

Quasi-binomial zero-inflated regression model suitable for variables with bounded support

In recent years, a variety of regression models, including zero-inflated and hurdle versions, have been proposed to explain the case of a dependent variable with respect to exogenous covariates. Apart from the classical Poisson, negative binomial and generalised Poisson distributions, many proposals have appeared in the statistical literature, perhaps in response to the new possibilities offered by advanced software that now enables researchers to implement numerous special functions in a relatively simple way. However, we believe that a significant research gap remains, since very little attention has been paid to the quasi-binomial distribution, which was first proposed over fifty years ago. We believe this distribution might constitute a valid alternative to existing regression models, in situations in which the variable has bounded support. Therefore, in this paper we present a zero-inflated regression model based on the quasi-binomial distribution, taking into account the moments and maximum likelihood estimators, and perform a score test to compare the zero-inflated quasi-binomial distribution with the zero-inflated binomial distribution, and the zero-inflated model with the homogeneous model (the model in which covariates are not considered). This analysis is illustrated with two data sets that are well known in the statistical literature and which contain a large number of zeros.     

Adherence to Mediterranean diet and risk of prostate cancer

In Europe, countries following the traditional Mediterranean Diet (MeDi), particularly Southern European countries, have lower prostate cancer (PCa) incidence and mortality compared to other European regions. In the present study, we investigated the association between the MeDi and the relative risk of PCa and tumor aggressiveness in a Spanish population. Among individual score components, it has been found that subjects with PCa were less likely to consume olive oil as the main culinary fat, vegetables, fruits and fish than those without. However, these differences were not statistically significative. A high intake of fruit, vegetables and cooked tomato sauce Mediterranean style (sofrito) was related to less PCa aggressiveness. Results showed that there are no differences in the score of adherence to the Mediterranean dietary patterns between cases and controls, with mean values of 8.37?±?1.80 and 8.25?±?2.48, respectively. However, MeDi was associated with lower PCa agressiveness according to Gleason score. Hence, relations between Mediterranean dietary patterns and PCa are still inconclusive and merit further investigations. Further large-scale studies are required to clarify the effect of MeDi on prostate health, in order to establish the role of this diet in the prevention of PCa.     

高等学校学生成绩分析方法的研究

学生的考试成绩一直是直接评价学生学业的重要标准,也是评价学生综合素质的一个主要指标。综合分析高等学校学生的学习成绩,掌握学生的学习动态,对培养学生成才至关重要。应用软件Microsoft Office Excel研究了综合分析普通高等学校学生成绩的方式,并将分析的结果应用到学生的培养。实践证明,该学习成绩的分析方法可以有效地提高学生的培养成效,在实际应用中可以作为培养学生成才的重要依据,为高等学校培养学生成才提供重要的分析工具。     

构建基于平衡计分卡的绩效评价与激励机制

平衡计分卡的每一项指标都包含着绩效驱动关系与激励因素。在平衡计分卡转化为行动的实施过程中引入激励机制,既实现了战略动态评价和管理,又通过财务、客户、内部流程、员工学习与成长四个层面的多种指标评价,揭示绩效产生的动因,激励企业的利益相关者,达到"评价什么就得到什么"的目标。